Because my cooperating teacher had me working with different math teachers in the building, she did not get to observe this lesson that I taught, but I was still able to talk to her before and after the lesson so she could help me plan what I was going to teach and to reflect on the lesson delivery. She urged me to use manipulatives to help the students make sense of what I was teaching and make the lesson more engaging. The manipulatives helped to provide a visual and physical representation of the concept of the Pythagorean Theorem while also helping the students to make sense of what I was saying since I was teaching in English. The students had already learned the Pythagorean Theorem and had some practice using it beforehand, which also helped them as they were able to bridge their pre-existing knowledge on the topic while connecting it new English terms and definitions.
Overall, I think the lesson went well. I was nervous about teaching a math lesson to middle schoolers because I had never done it before, and because I was teaching them in English. I started the lesson by having them tell me what they knew about the Pythagorean Theorem. I was able to call on students to show me what they know on the board rather than having to communicate it verbally and struggling with the language barrier. I then taught them the English terms and definitions, relating them to what they told me they knew. From there, I moved on to showing the students a proof. I found a great video on YouTube that showed a proof using paper, scissors and a ruler. I knew that all students would have these materials and felt that this would be a demonstration that we could easily do together as a class. The proof involved cutting out a right triangle and three squares to represent the length of each side of the triangle squared. In this way, the two smaller triangles would have to fit inside the big triangle in order to prove that a^2 + b^2 = c^2. I taught the same lesson twice, and the first time I taught it, I messed up the demonstration and it didn’t work. After I stumbled through an apology and attempted to explain my mistake, we moved on to working on word problem. I gave them the word problem: “Claire wants to hang a banner from the sill of a second-story window in her house. She needs to find a ladder that, when rested against the outside wall of her house will be long enough to reach the second-story window. If the window is 16 feet above the ground and Claire places the foot of the ladder 12 feet from the wall, how long will the ladder need to be?” I changed the vocabulary around a little bit to simplify it and went through the vocabulary words in the problem with them. Additionally, I drew a picture on the board to accompany the word problem and the math teacher who understood little English was still able to understand and supplement my English explanations with her Italian explanations. I was impressed by how easily the students seemed to comprehend the word problem and even more impressed by how quickly they were able to arrive at the answer.
Luckily, after my first lesson, I had an hour break and was able to figure out where my mistake was when attempting the demonstration the first time around. The second time I did my demonstration it went a lot more smoothly, and we had time to answer more word problems. I chose to use world problems because it integrated the learning of English vocabulary, and offered real-world applications of the Pythagorean Theorem. My second class went a lot more smoothly on my side, and in turn, the students were very engaged throughout as well.
Overall, teaching these math lessons was a great experience. It was a nice change of pace from teaching English lessons all the time and a good learning experience for me. Additionally, it was really interesting to get to work with other teachers in the building, and an interesting experience navigating the language barrier with them since I am used to working with the English teachers who speak perfect English and who I have no problems communicating with. I was very nervous about this, but I was touched by how kind and accommodating these teachers were, and felt really welcome as a guest teacher in their classrooms. Additionally, the students were very kind, even when my demonstration failed.